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Ancient solutions of Ricci flow with Type I curvature growth
Stephen Lynch, Andoni Royo Abrego
Ancient solutions of the Ricci flow arise naturally as models for singularity formation. There has been significant progress towards the classification of such solutions under natu…
Quadratically pinched submanifolds of the sphere via mean curvature flow with surgery
Mat Langford, Stephen Lynch, Huy The Nguyen
We study mean curvature flow of -dimensional submanifolds of , the round -sphere of sectional curvature , under the quadratic curvature pinching con…
Uniqueness of convex ancient solutions to hypersurface flows
Stephen Lynch
We show that every convex ancient solution of mean curvature flow with Type I curvature growth is either spherical, cylindrical, or planar. We then prove the corresponding statemen…
Convexity estimates for hypersurfaces moving by concave curvature functions
Stephen Lynch
We study fully nonlinear geometric flows that deform strictly -convex hypersurfaces in Euclidean space with pointwise normal speed given by a concave function of the principal c…
Pinched Ancient Solutions to the High Codimension Mean Curvature Flow
Stephen Lynch, Huy The Nguyen
We study solutions of high codimension mean curvature flow defined for all negative times, usually referred to as ancient solutions. We show that any compact ancient solution whose…